Stress-Constrained Thermo-Elastic Topology Optimization: A Topological Sensitivity Approach

Abstract

The focus of this paper is on thermo-elastic topology optimization where the structure is subject to both mechanical and thermal loads. Such problems are of significant importance, for example, in the aircraft industry where structures subject to aerodynamic forces and thermal-gradients must be optimized. A popular strategy for solving such problems is Solid Isotropic Material with Penalization (SIMP) where pseudo-densities serve as optimization parameters. Yet another strategy is the Rational Approximation of Material Properties (RAMP) that overcomes some of the deficiencies of SIMP. Both methods fundamentally rely on parameterization of the material properties as a function of the pseudo-densities. Here we consider an alternate level-set approach that relies on the concept of topological sensitivity. The advantages of the proposed method over SIMP and RAMP are: (1) ad hoc material parameterization is not required (2) the stresses are well-defined at all points within the evolving topology and (3) the underlying stiffness matrices are always well-conditioned. The proposed method is illustrated through numerical experiments.